RICERCA ITALIANA     

Understanding ab-initio the structural, electronic and optical properties of nanostructured and low-dimensional semiconductor systems

Università degli Studi di Modena e Reggio Emilia

Abstract

This project is aimed to integrate and develop the research capabilities of four teams having complementary expertises in the study of processes related to the electronic and optical properties of nanostructured and low-dimensional semiconductor systems. Such processes, which are very important both from the point of view of fundamental science and that of technological applications, will be studied at the atomic level, exploiting the now powerful combination of quantum-mechanical theory and computer simulation.

The theoretical understanding of the electronic states is a fundamental step for the design of new materials, being intimately linked with their experimental characterization. Many experimental quantities, obtained as the response to external probes in modern nondestructive spectroscopies, as photoemission, energy-loss, or optical absorption spectra, involve electronic excitations, and hence require a detailed knowledge of electronic excited states. It is, thus, critical to be able to describe accurately the latter with reliable and efficient theoretical approaches.

In order to reach our goals we will coordinate and combine the activities of four research groups. The latter are, since long time, active in this research field along timely and relevant lines, documented by the amount of high-profile publications. Besides being now among the world leading groups in the field, they have also demonstrated a strong availability and ability to collaborate.

This proposal connects state-of-the-art theoretical and computational development with its target application to nanostructured systems.

A primary purpose will be, in fact, the development of new theoretical and computational tools for an improved description of electron correlation and optical properties. These tools, mainly based on ab-initio density functional methods, are aimed to understand the interplay between the experimentally observed changes in optical properties and the related structural modifications of the material under study (e.g. nanostructuration, surface chemistry, surface reconstruction, etc.).

Moreover, we plan applications of these tools to several nanostructured and low-dimensional semiconductor systems, involved in many of the present cutting-edge developments: in nanotechnology, in semiconductor device fabrication, in quantum computing, or bio-functionalization, just to mention some of them. Specific systems have been chosen both for their potential applications in opto- and micro-electronics, and because they allow to isolate particular effects of the reduced dimensionality.

Many key-systems chosen are low-dimensional systems based on silicon: different Si surfaces and interfaces, porous silicon, Si quantum wires, and quantum dots. Most of them are important because of their recently discovered unconventional and exciting optical properties.

The methods successfully used for these key-systems will be applied to similar systems based on other semiconductors or materials, having strong technological potential: e.g., germanium nanostructures, composite polymers containing carbon nanotubes, semiconducting metal oxides, and organic-functionalized semiconductor surfaces. In many cases, the optical properties calculation for the systems under investigation will allows us to discriminate between the different proposed structural and growth models.

The results planned in this project will impact both fundamental and applied research. Our outcomes will be disseminated through publications in international journals, and, when possible, under the form of computer codes made available to the scientific community. We also expect a strong impact of our results in applied research on systems that are important for optoelectronics devices being fully compatible with conventional electronics, and in the general field of nanotechnology.

The success of this project will reinforce the leading position of Italy in this field. <<<

Principal Investigator

Stefano OSSICINI Università degli Studi di MODENA e REGGIO EMILIA

Research Objectives

The scientific aim of this research program is the substantial improvement and development of a theoretical approach "with atomic understanding" for the determination of the structural, electronic and optical properties of nanostructured and low-dimensional semiconductor systems.

To reach this goal this program will integrate and develop the research capabilities of four research teams in the field of the fundamental science of nanoscale systems and advanced materials. These teams have actively and succesfully collaborated in the past in several projects, such as the PRIN Ossicini 1997, PRIN Ossicini 2002, the CNR Project MADESS2, and the INFM-PRA Project RAMSES 2000 and the INFM-PAIS Project CELEX 2002. Moreover both Roma and Milano nodes already belong to an European Network of Excellence (NoE) entitled NANOQUANTA, whereas Modena and Napoli nodes are both active in the European Network Psi-k "Electronic Structure Calculation of Solids and Surfaces"; besides Ossicini is the European Coordinator of the submitted NoE Project "Silicon Nanophotonics".

Through the active collaboration and the powerful combination of quantum-mechanical theory and computer simulation we will make contact with nanoscience experimental studies and directly with technologically relevant structural, electronic and optical processes. Several state-of-the-art computer codes are available for the proposed research program: besides publicly available codes such as "ESPRESSO", "ABINIT", "FHI98MD", "LMTO", "FLAPW", or "OCTUPUS", we will use a number of computer codes developed, all or in part, whithin our groups. They range from optimized "Tight-Binding" codes with output for the calculation of the dielectric function, to Car-Parrinello-type DFT-LDA code (plane-wave and norm-conserving psudopotentials), to GW codes, methods for the solution of the Bethe-Salpeter equation and TDDFT codes.

We will strongly focus on the development of both theoretical and algorithmic methods. In particular we will use many-body perturbation theory and time-dependent density-functional theory (TDDFT), both methods have witnessed impressives advances in recent years. Moreover we will study excitation of nanoclusters using pair-excitation energies. Indeed all the different computational methods used will be compared in order to discriminate between them regarding the efficiency, the affidability, the ease of use , etc.. We intend, then, to exploit any possibility in order to study systems formed by a very high number of atoms.

The two goals of this Research Program are thus:
1) the development and numerical implementation of theoretical tools specific to the the many-body effects and the electronic excited states problem;
2) the application of our theoretical and computational tools to advanced materials: complex and nanostructured systems with reduced dimensionality ranging from 0 to 2.
The specific objectives of subject 1) are:
i) the calculation of the response functions within many-body perturbation theory using the GW approximation and the solution of the Bethe-Salpeter equation, which explicitely contains the dynamics of the electron-hole pairs. Here the important challenge is to develop approximations that boosts the efficiency without sacrificing its quantitative accuracy;
ii) the research and experimentation of new approximations for the TDDFT kernel. This achievement will open a route to the application of the TDDFT to systems and phenomena too complex to be studied within many-body perturbation theory;
iii) the calculation of excited state structural relaxations using the Constrained Density Functional method;
iv) the study of the electron-phonon interaction through the finite temperature Green function scheme;
v) the development of efficient semi-empirical approaches for the study of the optical properties of nanostructures with an huge number of atoms, that are not tractable within ab-initio approaches;
v) the development of efficient interfaces between different codes and the careful comparison between the different methods used.
The specific objectives for subject 2) are:
i) the study of the optical properties dependence of Si nanostructures (absorption and luminescence) on the dimensionality, the geometry and the surface chemistry. These studies are an important starting point for the understanding and modelling of the observed optical gain in Si nanocrystals;
ii) the study of doped nanocrystals and of the role of impurities on the optical and electronic properties of Si nanocrystals. Here the main objective is the understanding of electrical activity reactivation processes;
iii) the calculation of the optical properties of Ge and mixed Ge/Si nanostructures. Here we will study the size dependence of the optical spectra for Ge and Ge/Si quantum wires and quantum dots. In particular we will investigate the dependence of the optical properties on symmetry aspects, on the passivating agents of the dangling bonds at the interfaces, and on the structural rearrangements. The main goal here is to assess the best conditions in order to have bright light emission;
iv) the study of oxidized silicon surfaces. Through the calculation of the Reflectance Anisotropy and Surface Differential Reflectivity Spectra we will discuss the growth of thin (nanometer-scale) oxide films above clean Si(100) surfaces, of fundamental interest for the development of microlectronic devices;
v) the computation of the optical properties of several surfaces. Here the goal is to discriminate, using the computational outcomes, between the different suggested structural models;
vi) the computation of the optical properties of composite polymers containing carbon nanotubes. Coniugated polymers and its derivatives can form composites with carbon nanotubes, yielding films which are promising for potential applications like light emitting diodes;
vii) the study of the optical properties of organic molecules isolated and adsorbed on semiconductor nanostructures and surfaces. The goal here is to understand the possible role of these systems with respect to hybrid materials, molecular electronics, and bio-functionalisation.
The last and very important objective is the young researchers training to an high, international level. Several PhD students will participate to this project, moreover 140.900 Euro, more than the half cost of the entire project, will be used to hired young personnel. <<<

Timescale

24 months

National and international background

Understanding and controlling the properties of materials is crucial for improving the information technology on which our modern life is built. In particular, the ability to describe the electronic excitations with accurate ab-initio methods is of fundamental importance for the study of new materials. The theory plays a crucial role, not only from the point of view of the fundamental research, but also because a precise knowledge of the electronic excitations represents a fundamental step towards the innovation, design and fabrication of materials and devices based on nanoscale-technology having properties tuned to the requirements of real technological applications.
Although Density Functional Theory (DFT) [1] has proven to be a powerful tool for calculating electronic ground-state properties, it is of limited use for providing an accurate description of spectroscopic properties. For instance, it is well known that DFT underestimates the energy gaps, and only by overcoming the single particle approach [2] it is possible to obtain good agreement with the experimental data.



Fig. 1 Experimental gaps (dashed) compared with theoretical DFT-LDA ones (circles) and those within the GW method (squares) [3].

Thus DFT should be considered as a first step towards more sophisticated theoretical and computational schemes based on many-body perturbation theory (MBPT) or, alternatively, on time-dependent density-functional theory (TDDFT) [4,5]. These approaches open, in principle, a pathway towards calculation of the exact optical spectra and have advanced impressively. As such, both techniques represent the state-of-the-art of first-principles calculations of electronic excited states.
Although MBPT and TDDFT follow different philosophies, progress has been made by regarding them as complementary, and by comparing their strengths and weaknesses [5]. In MBPT key ingredients are the electron's self-energy [6,7] and the electron-hole (e-h) interaction; the calculation of response functions requires a solution of the Bethe-Salpeter equation (BSE) [8,19], which contains the dynamics of e-h pairs, created through absorption of a photon, in the form of appropriate Feynman diagrams.
The predictive power of MBPT can now be exploited for the study of realistic systems. An example is given by the Ge(111)(2x1) surface [10]: the study of its two lowest-energy isomers has suggested that the ground-state geometry of this surface corresponds to Pandey-like chains with a buckling angle opposite to that of the commonly assumed geometry. (see Fig. 2).



Fig.2. Ge(111)(2x1) Surface. Top panel: Pandey reconstruction, bottom panel: negative buckling

In Fig. 3, the Surface Differential Reflectivity Spectra (SDR) are reported for both isomers. The upper panel is for positively, while the lower panel is for negatively buckled chain. In both panels, the full (dashed) curves include (neglect) excitonic effects.



Fig.3. SDR Spectrum of the Ge(111)(2x1) surface, calculated for normal incidence. Top: Pandey reconstruction, bottom: negative buckling. Dots: experiment.

This prediction has been confirmed also by STM [11].

The MBPT spectra are very accurate and serve as a benchmark for other schemes, but the explicit diagrammatic approach makes the method numerically expensive and effectively restricts it to simple systems. An important challenge is, thus, to develop approximations that boost the efficiency of MBPT without sacrificing its accuracy. On the other hand, TDDFT [4,12,13] deals directly with global density-fluctuations resulting from external perturbations. The TDDFT approach leads hence to a screening equation similar to the BSE, but with a two-point, rather than a four-point, interaction kernel.



Fig. 4. Top: BSE (4 points kernel); bottom: TDDFT (2-points kernel)

Thus, this approach is much more efficient, but it is difficult to incorporate dynamic exchange-correlation effects. Much of the recent progress has resulted from a combination of these two methods.
Groups involved in this project have contributed to the development of a new TDDFT kernel, obtained from the BSE, that has been tested for several systems [14-18], at the same time an efficient TD method to solve the BSE has been developed [19]. Within the use of the new kernel is possible to reproduce experimental optical and EELS spectra [18].



Fig. 5. Absorption spectra calculated within the BSE (black), and the TDDFT (red) compared with experiments (blue circles) and with the independent QP calculation (dashed).

Although a number or fundamental questions remain unanswered, the theoretical foundations are well established, and it is now possible to treat low-dimensional materials, making contact with experimental and technologically relevant processes. Nevertheless, the prospect of future applications to more complex systems is connected to the exploitation of high-performance supercomputers and to the development of efficient parallel algorithms. To make an example, a recent numerical parallel implementation [20] for solving the BSE, has been shown to be essential for the calculation of optical spectra including excitonic and self-energy effects for many semiconductor surfaces where a large number of e-h pairs interfere and produce very large excitonic matrices which are very difficult, if not impossible, to diagonalize [21]. An excellent example of the usefulness of this method and of the need to include excitonic effects to obtain good agreement with experimental data is given by the calculation of the RAS of the diamond (100) surface. Only the inclusion of e-h interactions, revealing the presence of a surface exciton with a binding energy of 1 eV, is able to explain the experimental data [21].



Fig. 6. (a): experimental RAS. (b): dashed: theoretical RAS with GW; solid: theoretical RAS with GW, local-field and excitonic effects.

At the same level of complexity is the need of the development and application of advanced computational techniques for modelling the response properties of novel materials and artificial structures at the nanometer scale. These include the optical and doping properties of semiconductor quantum-wells, -wires and -dots. The reason is simple, many properties of nanocrystals (NC) may have significant and useful changes with respect to the bulk [22]. For example Si-NC have shown unexpected potentialities, even for optoelectronic applications [23]. It is worth mentioning the strong light emission from porous Si [24] and the recent observation of optical gain (OG) [25,26]. There still are many unanswered questions. It is worth citing the long standing debate on the origin of the strong light emission [22,23,27,28], the problem of doping and the role played by surface functionalization [29].
Bulk Si is not a good light emitter. However, in the nanometric phase, strongly improves its emission ability. Understanding this phenomenon implies the analysis of both ground and excited state of the NC. The theoretical investigation of phenomena such as the Stokes shift, the luminescence energy vs NC size and surface termination, etc., can give a fundamental contribution to the understanding of how tuning the optical response of such systems. A lot of work has been done dealing with excited NC, but a clear comprehension is lacking. Recently groups involved in this project have presented a comprehensive analysis Si-NC in both ground and excited states using DFT [28]. Excitation of NC has been studied calculating pair-excitation energies [30-32]. The formation of an e-h pair under excitation is taken into account, forcing one electron to occupy the LUMO, leaving a hole in the HOMO. A schematic representation is drawn in Fig. 7.



Fig. 7. Schematic representation of a Stokes shift relaxation.

A strong interplay between the NC structural and electronic properties comes out. Distortions induce the presence of new localised energy levels at the origin of the modification of the optical properties. The localisation of these states with respect to the atomic position in the NC is presented below.



Fig. 8. HOMO and LUMO square modulus contour plots.

Also for NC it is necessary to perform calculations of the opto-electronic properties using different methods to discriminate between them and to develop suitable routines. This has been done in a recent work, that shows the importance of the collaboration among our reasearch teams [33] . This Table shows the comparison between exp. and calc. energy gap for different Si-NC. The calculation have been performed using different ab-initio schemes.



Moreover the absorption spectra have been also calculated to compare MBPT and TDDFT outcomes.



Fig. 9. Absorption of the Si5H12 NC calculated using different approaches.


Also Si transistors are moving towards dimension of few nanometers, and there are new device design [34] which incorporate Si-NC. Moreover the possibility of a Si based laser suggested by the OG measurements on Si-NC [35-37] in SiO2 and the development of efficient carrier injection in Si-NC arrays [38] have attracted a lot of interest on matrix isolated NC. Interface states have been considered good candidates for explaining these outcomes. Thus the problem of the interface between the Si-NC and the host matrix has become fundamental. In literature calculations on Si-O systems have concerned with the surface chemistry of O using different models for the oxidized NC [39-41] or for the Si/SiO2 interface between Si and SiO2 layers [42,43]. Only two works have studied embedded NC but they were based either on simplified models [44] or on calculations without total energy minimization [45]. Recently we have presented the first ab-initio calculation for Si-NC in SiO2[39,46]. This is only a first step in order to mimic the real samples. But, despite its simplicity, a lot of interesting links to the experimental outcomes can be found [46]. Fig. 10 shows the stick and ball picture of the final relaxed supercell for the Si-NC embedded in SiO2.



Fig. 10.

The calculated band structure shows the presence of states related to the Si-NC revealing a strong interplay between the NC and the surrounding matrix.

Regarding nanostructured systems, it is important also to study the properties of nanostructures possessing a large number of atoms that are not tractable within ab-initio schemes. This is the case of very large NC or of quantum wires with large diameter. In these cases semi-empirical approaches are necessary. Among the many, the tight-binding (TB) [47-49] is very flexible, particularly for nanosystems which have a complex shape [50]. There are, however, some difficulties in determining the matrix elements for calculating dielectric functions. These difficulties can be solved with an high level of parameterisation. Fig. 11 shows the extinction coefficient,calculated with TB (blue) and compared with the experimental result [51] (red) for a Si-NC, almost spherical, with diameters d=1.83 nm.



Fig. 11.

These data show that within TB it is possible to have a realistic description of the optical properties.

The possibility of enhancing the electrical conductivity of nanosized systems has been largely studied. For example, it is known that porous Si is obtained from bulk n- or p-doped Si by means of an electrochemical etching. Nevertheless, even for the larger samples, a low conductivity is measured, despite the etching process does not remove the impurities[52]. This suggests that the ionisation of the impurities is quenched with respect to the bulk. Thus, the possibility of generating free carriers from defect states is limited by size effects in NC, even if it has been shown that reactivation of carriers is possible [53-55]. An understanding of the trapping and detrapping mechanisms has not yet been reached. Since impurity doping is expected to change significantly the opto-electronic structure of doped NC, there is a need of a detailed theoretical knowledge of their properties. Very few theoretical atomistic studies concerning impurity states in NC are present in the literature, mostly based on semi-empirical approaches [56]. Quantum confinement in phosphorous-doped Si-NC has been analyzed in [57], using ab-initio DFT. These results point out that the ionization energy for the doped NC is virtually size independent.
The physical mechanism according to which molecules like NO2 and NH3 [53-55] are able of reactivating conductivity is not clear. It is likely important the position of the impuritiy inside the NC. Some results of ab-initio calculations of the boron formation energies in Si-NC are shown in Fig.12 [58].



Fig. 12.

The formation energy has been computed considering different substitutional positions indicated in the part (a) of the figure, whereas in the part (b) the corresponding energies are shown. The interesting data is that the formation energy gets low going towards the surface. This result may be very important for the comprehension of the reactivation mechanism.

The bio-functionalization of semiconductor surfaces has been emerging as an important field and has been recognized as a way of adding new functionality to surfaces [29,59]. One can foresee devices whose width is reduced down to few atomic layers so that most of their functionalities are due to phenomena occurring at or near the surface. It is believed that hybrid organic-semiconductor materials may have potentiality for applications in molecular electronics, computing, sensing, etc. [60]. The Si(001) surface is characterized by adjacent atoms forming ordered rows of dimers [61]. The bonding within a dimer can be viewed as a double bond. This circumstance is of great interest because it suggests an analogy between dimer and C=C double bond so that an unsaturated organic molecule can bind on a Si dimer [60]. This anchoring mechanism has been experimented for binding a number of organic molecules on the Si(001) surface [29,60,61]. We have studied the adsorption of 1-amino-3-cyclopentene on Si(001) [62]. The characteristic of this molecule is the presence of a C=C double bond and of an primary amine functionality useful for DNA anchoring on Si [63]. Fig. 13 shows the calculated reaction path on a Si dimer.



Fig. 13.

These results show, in accordance with experiment [59], that this type of reaction does not need big thermal activation energies. Moreover, it is possible to obtain an organic layer with a translational order. Ordered molecular ensembles often have unusual properties and advanced ab-initio calculations have been performed [64].

The interest on metal oxides has been growing recently thanks to synthesis techniques able to produce single crystal nanobelts [65]. Nanobelts of semiconducting oxide are very promising for sensors due to the high surface to volume ratio. Fig. 14 shows a TEM image of SnO2 nanobelts [66].



Fig. 14.

These nanostructures have interesting opto-electronic properties, different from those of polycrystalline films. The surface energetic is one of the key nodes for the comprehension of these systems. Ab-initio calculations show that the surface energy tend to increase on increasing the number of oxygen vacancies. The oxygen dynamics is one of the main topics for these materials [67].
Also nanostructured semiconductor based on Si are important for the study of the interaction and the selective detection of bio-chemical quantities. DFT is particularly useful in understanding how a given organic molecule is adsorbed on a semiconductor NC [68].

In conclusion, in all these fields, there is a need for improvement, in particular towards the development of a theoretical approach "with atomic understanding". <<<